As mentioned in the introduction, an important open issue in LQC is its connection with LQG [1]}. In particular, in LQC the spacetime symmetry is first imposed (in the classical level), before
the quantization process is carried out. However, it is well-known that this is different from the general process of LQG [2]}, and as a result, different Hamiltonian constraints could be resulted,
hence resulting in different Planck scale physics.
Though the question of ambiguities in obtaining the Hamiltonian in LQG is still open, based on some rigorous proposals by Thiemann [3]},
various attempts have been carried out, in order to obtain deeper insights into the question.
